Preheat oven 425 degrees. Line a baking sheet with foil. Toss the potatoes with oil salt and pepper. Roast in oven for about 20 minutes stirring occasionally.
Meanwhile melt the butter in a saute pan and add the mushrooms let cook about 10 minutes. Add the garlic and miso paste. Cook for 1 minute add the white wine and let most evaporate. Add the heavy cream and cheese. Taste and adjust for salt and pepper. Sprinkle with the thyme.